digraph physicsDerivation { 
overlap = false;
label="derivation: optics: Law of refraction to Brewster's angle
https://allofphysiscs.com";
fontsize=12;
0007919446 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_declareinitialexpression.png",labelloc=b];
0007919446 -> generated_expression_8945218208_d5a66fe8eb0ea1cf2e5537c9ad3b448015f82cd72327d206b094062061c955f4;
generated_expression_8945218208_d5a66fe8eb0ea1cf2e5537c9ad3b448015f82cd72327d206b094062061c955f4 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_8945218208_d5a66fe8eb0ea1cf2e5537c9ad3b448015f82cd72327d206b094062061c955f4.png",labelloc=b];
0009582699 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_subtractXfrombothsides.png",labelloc=b];
generated_expression_8945218208_d5a66fe8eb0ea1cf2e5537c9ad3b448015f82cd72327d206b094062061c955f4 -> 0009582699;
generated_expression_8945218208_d5a66fe8eb0ea1cf2e5537c9ad3b448015f82cd72327d206b094062061c955f4 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_8945218208_d5a66fe8eb0ea1cf2e5537c9ad3b448015f82cd72327d206b094062061c955f4.png",labelloc=b];
0009582699 -> generated_expression_1310571337_00b559ab2d4eb4799dbacf0a0aab096956e5e9c7894b8796531489c764c214b9;
generated_expression_1310571337_00b559ab2d4eb4799dbacf0a0aab096956e5e9c7894b8796531489c764c214b9 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_1310571337_00b559ab2d4eb4799dbacf0a0aab096956e5e9c7894b8796531489c764c214b9.png",labelloc=b];
generated_feed_9025853427_c5045b20ea95b9f34024082e6af9d4277514171218e69bb468fcf98ec86baddf -> 0009582699;
generated_feed_9025853427_c5045b20ea95b9f34024082e6af9d4277514171218e69bb468fcf98ec86baddf [shape=box, color=red,label="",image="/code/static/generated_feed_9025853427_c5045b20ea95b9f34024082e6af9d4277514171218e69bb468fcf98ec86baddf.png",labelloc=b];
0002215432 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_declareinitialexpression.png",labelloc=b];
0002215432 -> generated_expression_6450985774_d9b2f7f5418d4dda069469b54ecdc2a57a5f5308631ef521570da2e7a3fd11a8;
generated_expression_6450985774_d9b2f7f5418d4dda069469b54ecdc2a57a5f5308631ef521570da2e7a3fd11a8 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_6450985774_d9b2f7f5418d4dda069469b54ecdc2a57a5f5308631ef521570da2e7a3fd11a8.png",labelloc=b];
0005372769 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_changetwovariablesinexpression.png",labelloc=b];
generated_expression_6450985774_d9b2f7f5418d4dda069469b54ecdc2a57a5f5308631ef521570da2e7a3fd11a8 -> 0005372769;
generated_expression_6450985774_d9b2f7f5418d4dda069469b54ecdc2a57a5f5308631ef521570da2e7a3fd11a8 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_6450985774_d9b2f7f5418d4dda069469b54ecdc2a57a5f5308631ef521570da2e7a3fd11a8.png",labelloc=b];
0005372769 -> generated_expression_2575937347_bbf7b7034cde9f30c717efb9e904393c0df65fd1c4a814c79ec8c7b37cf9cf1f;
generated_expression_2575937347_bbf7b7034cde9f30c717efb9e904393c0df65fd1c4a814c79ec8c7b37cf9cf1f [shape=ellipse, color=black,label="",image="/code/static/generated_expression_2575937347_bbf7b7034cde9f30c717efb9e904393c0df65fd1c4a814c79ec8c7b37cf9cf1f.png",labelloc=b];
generated_feed_9029795851_c5045b20ea95b9f34024082e6af9d4277514171218e69bb468fcf98ec86baddf -> 0005372769;
generated_feed_9029795851_c5045b20ea95b9f34024082e6af9d4277514171218e69bb468fcf98ec86baddf [shape=box, color=red,label="",image="/code/static/generated_feed_9029795851_c5045b20ea95b9f34024082e6af9d4277514171218e69bb468fcf98ec86baddf.png",labelloc=b];
generated_feed_2773628333_9f146cf9b0e1580ea528a45cee21c255ed06ee733f693b5fd7ff47a3b6db57f7 -> 0005372769;
generated_feed_2773628333_9f146cf9b0e1580ea528a45cee21c255ed06ee733f693b5fd7ff47a3b6db57f7 [shape=box, color=red,label="",image="/code/static/generated_feed_2773628333_9f146cf9b0e1580ea528a45cee21c255ed06ee733f693b5fd7ff47a3b6db57f7.png",labelloc=b];
generated_feed_6353701615_203be1363cf6c6cec00abfb31f21bb2a24d62441547123f36247d30a748e217f -> 0005372769;
generated_feed_6353701615_203be1363cf6c6cec00abfb31f21bb2a24d62441547123f36247d30a748e217f [shape=box, color=red,label="",image="/code/static/generated_feed_6353701615_203be1363cf6c6cec00abfb31f21bb2a24d62441547123f36247d30a748e217f.png",labelloc=b];
generated_feed_7154592211_d74d781424901ae1ffa660a4070e7d2021e91a2efb7ebcc53e8037aa118665de -> 0005372769;
generated_feed_7154592211_d74d781424901ae1ffa660a4070e7d2021e91a2efb7ebcc53e8037aa118665de [shape=box, color=red,label="",image="/code/static/generated_feed_7154592211_d74d781424901ae1ffa660a4070e7d2021e91a2efb7ebcc53e8037aa118665de.png",labelloc=b];
0005001869 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_substituteLHSofexpr1intoexpr2.png",labelloc=b];
generated_expression_2575937347_bbf7b7034cde9f30c717efb9e904393c0df65fd1c4a814c79ec8c7b37cf9cf1f -> 0005001869;
generated_expression_2575937347_bbf7b7034cde9f30c717efb9e904393c0df65fd1c4a814c79ec8c7b37cf9cf1f [shape=ellipse, color=black,label="",image="/code/static/generated_expression_2575937347_bbf7b7034cde9f30c717efb9e904393c0df65fd1c4a814c79ec8c7b37cf9cf1f.png",labelloc=b];
generated_expression_1310571337_00b559ab2d4eb4799dbacf0a0aab096956e5e9c7894b8796531489c764c214b9 -> 0005001869;
generated_expression_1310571337_00b559ab2d4eb4799dbacf0a0aab096956e5e9c7894b8796531489c764c214b9 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_1310571337_00b559ab2d4eb4799dbacf0a0aab096956e5e9c7894b8796531489c764c214b9.png",labelloc=b];
0005001869 -> generated_expression_7696214507_ff07ad77520359b2806655c4075c144d6df3b05d7464b0dd69efe8e47f4048f2;
generated_expression_7696214507_ff07ad77520359b2806655c4075c144d6df3b05d7464b0dd69efe8e47f4048f2 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_7696214507_ff07ad77520359b2806655c4075c144d6df3b05d7464b0dd69efe8e47f4048f2.png",labelloc=b];
0001148993 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_declareidentity.png",labelloc=b];
0001148993 -> generated_expression_8588429722_a7bf02f75f26fdf72aadc1f77f48317ecb26033dee41380cf2d6b30169964dbc;
generated_expression_8588429722_a7bf02f75f26fdf72aadc1f77f48317ecb26033dee41380cf2d6b30169964dbc [shape=ellipse, color=black,label="",image="/code/static/generated_expression_8588429722_a7bf02f75f26fdf72aadc1f77f48317ecb26033dee41380cf2d6b30169964dbc.png",labelloc=b];
0009056504 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_changevariableXtoY.png",labelloc=b];
generated_expression_8588429722_a7bf02f75f26fdf72aadc1f77f48317ecb26033dee41380cf2d6b30169964dbc -> 0009056504;
generated_expression_8588429722_a7bf02f75f26fdf72aadc1f77f48317ecb26033dee41380cf2d6b30169964dbc [shape=ellipse, color=black,label="",image="/code/static/generated_expression_8588429722_a7bf02f75f26fdf72aadc1f77f48317ecb26033dee41380cf2d6b30169964dbc.png",labelloc=b];
0009056504 -> generated_expression_6831637424_253efbf9a08fc8490dd5ce69aa15ad03b412884097a3e7082e78eb988c855d5c;
generated_expression_6831637424_253efbf9a08fc8490dd5ce69aa15ad03b412884097a3e7082e78eb988c855d5c [shape=ellipse, color=black,label="",image="/code/static/generated_expression_6831637424_253efbf9a08fc8490dd5ce69aa15ad03b412884097a3e7082e78eb988c855d5c.png",labelloc=b];
generated_feed_1512581563_2d711642b726b04401627ca9fbac32f5c8530fb1903cc4db02258717921a4881 -> 0009056504;
generated_feed_1512581563_2d711642b726b04401627ca9fbac32f5c8530fb1903cc4db02258717921a4881 [shape=box, color=red,label="",image="/code/static/generated_feed_1512581563_2d711642b726b04401627ca9fbac32f5c8530fb1903cc4db02258717921a4881.png",labelloc=b];
generated_feed_7375348852_c5045b20ea95b9f34024082e6af9d4277514171218e69bb468fcf98ec86baddf -> 0009056504;
generated_feed_7375348852_c5045b20ea95b9f34024082e6af9d4277514171218e69bb468fcf98ec86baddf [shape=box, color=red,label="",image="/code/static/generated_feed_7375348852_c5045b20ea95b9f34024082e6af9d4277514171218e69bb468fcf98ec86baddf.png",labelloc=b];
0001206301 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_substituteLHSofexpr1intoexpr2.png",labelloc=b];
generated_expression_7696214507_ff07ad77520359b2806655c4075c144d6df3b05d7464b0dd69efe8e47f4048f2 -> 0001206301;
generated_expression_7696214507_ff07ad77520359b2806655c4075c144d6df3b05d7464b0dd69efe8e47f4048f2 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_7696214507_ff07ad77520359b2806655c4075c144d6df3b05d7464b0dd69efe8e47f4048f2.png",labelloc=b];
generated_expression_6831637424_253efbf9a08fc8490dd5ce69aa15ad03b412884097a3e7082e78eb988c855d5c -> 0001206301;
generated_expression_6831637424_253efbf9a08fc8490dd5ce69aa15ad03b412884097a3e7082e78eb988c855d5c [shape=ellipse, color=black,label="",image="/code/static/generated_expression_6831637424_253efbf9a08fc8490dd5ce69aa15ad03b412884097a3e7082e78eb988c855d5c.png",labelloc=b];
0001206301 -> generated_expression_3061811650_f851ddc4ae2f41f8c46ec4a587c48497c326bd94384f71f985710d198c14a98d;
generated_expression_3061811650_f851ddc4ae2f41f8c46ec4a587c48497c326bd94384f71f985710d198c14a98d [shape=ellipse, color=black,label="",image="/code/static/generated_expression_3061811650_f851ddc4ae2f41f8c46ec4a587c48497c326bd94384f71f985710d198c14a98d.png",labelloc=b];
0003169869 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_dividebothsidesby.png",labelloc=b];
generated_expression_3061811650_f851ddc4ae2f41f8c46ec4a587c48497c326bd94384f71f985710d198c14a98d -> 0003169869;
generated_expression_3061811650_f851ddc4ae2f41f8c46ec4a587c48497c326bd94384f71f985710d198c14a98d [shape=ellipse, color=black,label="",image="/code/static/generated_expression_3061811650_f851ddc4ae2f41f8c46ec4a587c48497c326bd94384f71f985710d198c14a98d.png",labelloc=b];
0003169869 -> generated_expression_9756089533_1e49980dc9d9275976c6e22af39dcd5ccd4081ece55d7eb5efefddfc931ba9d9;
generated_expression_9756089533_1e49980dc9d9275976c6e22af39dcd5ccd4081ece55d7eb5efefddfc931ba9d9 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_9756089533_1e49980dc9d9275976c6e22af39dcd5ccd4081ece55d7eb5efefddfc931ba9d9.png",labelloc=b];
generated_feed_7857757625_583292a11ba243814acf172b4541fe1b5817b1f8f9ffa5068b23f57f3996d407 -> 0003169869;
generated_feed_7857757625_583292a11ba243814acf172b4541fe1b5817b1f8f9ffa5068b23f57f3996d407 [shape=box, color=red,label="",image="/code/static/generated_feed_7857757625_583292a11ba243814acf172b4541fe1b5817b1f8f9ffa5068b23f57f3996d407.png",labelloc=b];
0008509796 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_dividebothsidesby.png",labelloc=b];
generated_expression_9756089533_1e49980dc9d9275976c6e22af39dcd5ccd4081ece55d7eb5efefddfc931ba9d9 -> 0008509796;
generated_expression_9756089533_1e49980dc9d9275976c6e22af39dcd5ccd4081ece55d7eb5efefddfc931ba9d9 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_9756089533_1e49980dc9d9275976c6e22af39dcd5ccd4081ece55d7eb5efefddfc931ba9d9.png",labelloc=b];
0008509796 -> generated_expression_2768857871_14cff2d2c843e3ca41fcb62c687936f61119bbbf8b925b2835c309a3bf2fe2a2;
generated_expression_2768857871_14cff2d2c843e3ca41fcb62c687936f61119bbbf8b925b2835c309a3bf2fe2a2 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_2768857871_14cff2d2c843e3ca41fcb62c687936f61119bbbf8b925b2835c309a3bf2fe2a2.png",labelloc=b];
generated_feed_5632428182_fbcf31678069c16e1f2add1f00bbd1ea96f6784b03acfea36ce6b6917b247d9b -> 0008509796;
generated_feed_5632428182_fbcf31678069c16e1f2add1f00bbd1ea96f6784b03acfea36ce6b6917b247d9b [shape=box, color=red,label="",image="/code/static/generated_feed_5632428182_fbcf31678069c16e1f2add1f00bbd1ea96f6784b03acfea36ce6b6917b247d9b.png",labelloc=b];
0002967028 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_declareidentity.png",labelloc=b];
0002967028 -> generated_expression_4968680693_5de8e84827969bb69596a42d7fb4c53bbb10f8f6ea46efaa44d6fbc534ec2dd2;
generated_expression_4968680693_5de8e84827969bb69596a42d7fb4c53bbb10f8f6ea46efaa44d6fbc534ec2dd2 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_4968680693_5de8e84827969bb69596a42d7fb4c53bbb10f8f6ea46efaa44d6fbc534ec2dd2.png",labelloc=b];
0006119314 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_changevariableXtoY.png",labelloc=b];
generated_expression_4968680693_5de8e84827969bb69596a42d7fb4c53bbb10f8f6ea46efaa44d6fbc534ec2dd2 -> 0006119314;
generated_expression_4968680693_5de8e84827969bb69596a42d7fb4c53bbb10f8f6ea46efaa44d6fbc534ec2dd2 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_4968680693_5de8e84827969bb69596a42d7fb4c53bbb10f8f6ea46efaa44d6fbc534ec2dd2.png",labelloc=b];
0006119314 -> generated_expression_4501377629_bccb7a6388a2ddab3a2c07290f5c89b2ee84838b25c8f324e06fb4b9ee34799e;
generated_expression_4501377629_bccb7a6388a2ddab3a2c07290f5c89b2ee84838b25c8f324e06fb4b9ee34799e [shape=ellipse, color=black,label="",image="/code/static/generated_expression_4501377629_bccb7a6388a2ddab3a2c07290f5c89b2ee84838b25c8f324e06fb4b9ee34799e.png",labelloc=b];
generated_feed_9906920183_2d711642b726b04401627ca9fbac32f5c8530fb1903cc4db02258717921a4881 -> 0006119314;
generated_feed_9906920183_2d711642b726b04401627ca9fbac32f5c8530fb1903cc4db02258717921a4881 [shape=box, color=red,label="",image="/code/static/generated_feed_9906920183_2d711642b726b04401627ca9fbac32f5c8530fb1903cc4db02258717921a4881.png",labelloc=b];
generated_feed_7321695558_c5045b20ea95b9f34024082e6af9d4277514171218e69bb468fcf98ec86baddf -> 0006119314;
generated_feed_7321695558_c5045b20ea95b9f34024082e6af9d4277514171218e69bb468fcf98ec86baddf [shape=box, color=red,label="",image="/code/static/generated_feed_7321695558_c5045b20ea95b9f34024082e6af9d4277514171218e69bb468fcf98ec86baddf.png",labelloc=b];
0006146931 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_substituteLHSofexpr1intoexpr2.png",labelloc=b];
generated_expression_2768857871_14cff2d2c843e3ca41fcb62c687936f61119bbbf8b925b2835c309a3bf2fe2a2 -> 0006146931;
generated_expression_2768857871_14cff2d2c843e3ca41fcb62c687936f61119bbbf8b925b2835c309a3bf2fe2a2 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_2768857871_14cff2d2c843e3ca41fcb62c687936f61119bbbf8b925b2835c309a3bf2fe2a2.png",labelloc=b];
generated_expression_4501377629_bccb7a6388a2ddab3a2c07290f5c89b2ee84838b25c8f324e06fb4b9ee34799e -> 0006146931;
generated_expression_4501377629_bccb7a6388a2ddab3a2c07290f5c89b2ee84838b25c8f324e06fb4b9ee34799e [shape=ellipse, color=black,label="",image="/code/static/generated_expression_4501377629_bccb7a6388a2ddab3a2c07290f5c89b2ee84838b25c8f324e06fb4b9ee34799e.png",labelloc=b];
0006146931 -> generated_expression_3417126140_848ab6397dd454750f437918799ec8576d0cda8038365e5a15b7682d0d5c7e23;
generated_expression_3417126140_848ab6397dd454750f437918799ec8576d0cda8038365e5a15b7682d0d5c7e23 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_3417126140_848ab6397dd454750f437918799ec8576d0cda8038365e5a15b7682d0d5c7e23.png",labelloc=b];
0008072315 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_applyfunctiontobothsidesofexpression.png",labelloc=b];
generated_expression_3417126140_848ab6397dd454750f437918799ec8576d0cda8038365e5a15b7682d0d5c7e23 -> 0008072315;
generated_expression_3417126140_848ab6397dd454750f437918799ec8576d0cda8038365e5a15b7682d0d5c7e23 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_3417126140_848ab6397dd454750f437918799ec8576d0cda8038365e5a15b7682d0d5c7e23.png",labelloc=b];
0008072315 -> generated_expression_8495187962_b287a50bbd6a3c743c8be3acfcdbf2daa2826b9c59592b9d7fce8bed67117e60;
generated_expression_8495187962_b287a50bbd6a3c743c8be3acfcdbf2daa2826b9c59592b9d7fce8bed67117e60 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_8495187962_b287a50bbd6a3c743c8be3acfcdbf2daa2826b9c59592b9d7fce8bed67117e60.png",labelloc=b];
generated_feed_6023986360_2d711642b726b04401627ca9fbac32f5c8530fb1903cc4db02258717921a4881 -> 0008072315;
generated_feed_6023986360_2d711642b726b04401627ca9fbac32f5c8530fb1903cc4db02258717921a4881 [shape=box, color=red,label="",image="/code/static/generated_feed_6023986360_2d711642b726b04401627ca9fbac32f5c8530fb1903cc4db02258717921a4881.png",labelloc=b];
generated_feed_5453995431_8edfe90d75cd8160e41fa2f9c5905bf5f6c1b91b67b1628ed7c33de464e67d58 -> 0008072315;
generated_feed_5453995431_8edfe90d75cd8160e41fa2f9c5905bf5f6c1b91b67b1628ed7c33de464e67d58 [shape=box, color=red,label="",image="/code/static/generated_feed_5453995431_8edfe90d75cd8160e41fa2f9c5905bf5f6c1b91b67b1628ed7c33de464e67d58.png",labelloc=b];
0002068603 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_declarefinalexpression.png",labelloc=b];
generated_expression_8495187962_b287a50bbd6a3c743c8be3acfcdbf2daa2826b9c59592b9d7fce8bed67117e60 -> 0002068603;
generated_expression_8495187962_b287a50bbd6a3c743c8be3acfcdbf2daa2826b9c59592b9d7fce8bed67117e60 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_8495187962_b287a50bbd6a3c743c8be3acfcdbf2daa2826b9c59592b9d7fce8bed67117e60.png",labelloc=b];
}